# Probabilistic forecast

Last updated August 14, 2023

## What is a probabilistic forecast?

A probabilistic forecast is a type of forecast that provides a range of possible outcomes or probabilities of future events, rather than a single point estimate. In other words, it provides an estimate of the likelihood of different scenarios or outcomes based on statistical models and historical data.

## When are probabilistic forecasts used?

Probabilistic forecasts are often used in situations where the future is uncertain and there are multiple possible outcomes, such as demand forecasting. Unlike a deterministic forecast, which provides a single point of estimate of future events, a probabilistic forecast accounts for the uncertainty and variability of the underlying data and provides a more realistic and comprehensive view of the future.

## How are they visualized?

A probabilistic forecast can take different forms depending on the specific context and goals of the forecasting problem. For example, it can be expressed as a range of possible values, such as a or a prediction interval, which indicates the level of uncertainty associated with the forecast. Alternatively, it can be expressed as a probability distribution, such as a normal distribution or a Poisson distribution, which provides a more detailed view of the possible outcomes and their likelihoods.

## Here's an example

Let’s say a retailer wants to forecast the demand for a new product that they plan to introduce in the market. The retailer collects historical sales data for similar products, as well as market research and other relevant information about the product’s features, pricing, and promotional activities. Based on this data, the retailer develops a statistical model that estimates the probability distribution of the demand for the new product for each month of the next year.

The model outputs a range of possible demand values for each month, along with their probabilities, based on the historical data and other factors.

For example, the model might predict that the demand for the new product in the first month will follow a normal distribution with a mean of 1000 units and a standard deviation of 200 units. This means that there is a 68% chance that the demand will fall within the range of 800 to 1200 units, and a 95% chance that it will fall within the range of 600 to 1400 units.